Assign shortcuts to different values from thedrop-down menu "Merge"
To make merging vertices faster change in User Preferences setup for this shortcut enabling Type option just below the main options:



Select the desired type from the list  to make this shortcut execute command with given option and skip any dialogs (most likely you will want to create also shortcuts to use other options of the operator).
To disable that either restore settings or press on X button near the Type selector. Read more details on this technique in this post - How To NOT extend selection with Box Select?.

However you have other approaches available too without need to change shortcuts.

One approach would be to use Shift+R to repeat the last action. So you would select 3 vertices in desired order, choose needed option from menu and then after selecting next verts just execute Repeat Last.

Anotehr way would be using list of Undo history from F3. Once doing any action it will be accessible from that list and you will be able to repeat it by pressing F3 > Enter. See more here - Is there a shortcut to repeat the last operation in Blender.

Also you could just choose another way of modeling and dissolve those vertices either with X > Limited Dissolve or Dissolve Edges (make sure to select needed geometry first).